The invention is based on an apparatus for measuring the mass of a flowing medium as defined generally hereinafter. In apparatuses of this type, the problem exists of securing the temperature-dependent resistor in such a manner that the least possible amount of heat is conducted via the holder, in order to assure rapid response times on the part of the apparatus. Furthermore, the temperature-dependent resistor should be disposed in the flow of the medium in as streamlined a manner as possible to prevent flow separations and associated undesirable changes in the measuring characteristic of the apparatus and to prevent excessive mechanical strain.